LLMs-Pharmaceutical / Git / [404218] /Code/PennyLane/Benchmarking Devices II/lightning.qubit 25 qubit TPU 127.59s (1) kkawchak.ipynb

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[404218]: / Code / PennyLane / Benchmarking Devices II / lightning.qubit 25 qubit TPU 127.59s (1) kkawchak.ipynb
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{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 87,
      "metadata": {
        "id": "rqYMIG5_jAmf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "outputId": "da6a2b9d-67c0-4631-99c2-a5b010e4b63a"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since beginning of run: 1701147930.5770738\n",
            "Tue Nov 28 05:05:30 2023\n"
          ]
        }
      ],
      "source": [
        "# This cell is added by sphinx-gallery\n",
        "# It can be customized to whatever you like\n",
        "%matplotlib inline\n",
        "\n",
        "# !pip install pennylane\n",
        "\n",
        "import time\n",
        "seconds = time.time()\n",
        "print(\"Time in seconds since beginning of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 88,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "30MBcn8AjAmh",
        "outputId": "6673a675-d39c-419d-946e-37391ffb7288"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.2  0.21 0.78]\n",
            " [0.21 0.15 0.89]\n",
            " [0.78 0.89 0.98]]\n"
          ]
        }
      ],
      "source": [
        "import numpy as np\n",
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "def create_data_point(n):\n",
        "    \"\"\"\n",
        "    Returns a random undirected adjacency matrix of dimension (n,n).\n",
        "    The diagonal elements are interpreted as node attributes.\n",
        "    \"\"\"\n",
        "    mat = np.random.rand(n, n)\n",
        "    A = (mat + np.transpose(mat))/2\n",
        "    return np.round(A, decimals=2)\n",
        "\n",
        "A = create_data_point(3)\n",
        "print(A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fZNWu6j_jAmh"
      },
      "source": [
        "Let\\'s also write a function to generate permuted versions of this\n",
        "adjacency matrix.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 89,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "9AlMlrsVjAmi",
        "outputId": "0f71e376-58af-4c0d-80a9-dd77498a4502"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[0.15 0.89 0.21]\n",
            " [0.89 0.98 0.78]\n",
            " [0.21 0.78 0.2 ]]\n"
          ]
        }
      ],
      "source": [
        "def permute(A, permutation):\n",
        "    \"\"\"\n",
        "    Returns a copy of A with rows and columns swapped according to permutation.\n",
        "    For example, the permutation [1, 2, 0] swaps 0->1, 1->2, 2->0.\n",
        "    \"\"\"\n",
        "\n",
        "    P = np.zeros((len(A), len(A)))\n",
        "    for i,j in enumerate(permutation):\n",
        "        P[i,j] = 1\n",
        "\n",
        "    return P @ A @ np.transpose(P)\n",
        "\n",
        "A_perm = permute(A, [1, 2, 0])\n",
        "print(A_perm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Js9CqRTZjAmi"
      },
      "source": [
        "If we create [networkx]{.title-ref} graphs from both adjacency matrices\n",
        "and plot them, we see that they are identical as claimed.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 90,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "Q7N1C_MKjAmi",
        "outputId": "3fb37eb9-c740-4593-bcff-40b30aee7ecc"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "fig, (ax1, ax2) = plt.subplots(1, 2)\n",
        "\n",
        "# interpret diagonal of matrix as node attributes\n",
        "node_labels = {n: A[n,n] for n in range(len(A))}\n",
        "np.fill_diagonal(A, np.zeros(len(A)))\n",
        "\n",
        "G1 = nx.Graph(A)\n",
        "pos1=nx.spring_layout(G1)\n",
        "nx.draw(G1, pos1, labels=node_labels, ax=ax1, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G1,'weight')\n",
        "nx.draw_networkx_edge_labels(G1,pos1,edge_labels=edge_labels, ax=ax1)\n",
        "\n",
        "# interpret diagonal of permuted matrix as node attributes\n",
        "node_labels = {n: A_perm[n,n] for n in range(len(A_perm))}\n",
        "np.fill_diagonal(A_perm, np.zeros(len(A)))\n",
        "\n",
        "G2 = nx.Graph(A_perm)\n",
        "pos2=nx.spring_layout(G2)\n",
        "nx.draw(G2, pos2, labels=node_labels, ax=ax2, node_size = 800, node_color = \"#ACE3FF\")\n",
        "edge_labels = nx.get_edge_attributes(G2,'weight')\n",
        "nx.draw_networkx_edge_labels(G2,pos2,edge_labels=edge_labels, ax=ax2)\n",
        "\n",
        "ax1.set_xlim([1.2*x for x in ax1.get_xlim()])\n",
        "ax2.set_xlim([1.2*x for x in ax2.get_xlim()])\n",
        "plt.tight_layout()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 91,
      "metadata": {
        "id": "eUhWZ9_3jAmi"
      },
      "outputs": [],
      "source": [
        "import pennylane as qml\n",
        "\n",
        "def perm_equivariant_embedding(A, betas, gammas):\n",
        "    \"\"\"\n",
        "    Ansatz to embedd a graph with node and edge weights into a quantum state.\n",
        "\n",
        "    The adjacency matrix A contains the edge weights on the off-diagonal,\n",
        "    as well as the node attributes on the diagonal.\n",
        "\n",
        "    The embedding contains trainable weights 'betas' and 'gammas'.\n",
        "    \"\"\"\n",
        "    n_nodes = len(A)\n",
        "    n_layers = len(betas) # infer the number of layers from the parameters\n",
        "\n",
        "    # initialise in the plus state\n",
        "    for i in range(n_nodes):\n",
        "        qml.Hadamard(i)\n",
        "\n",
        "    for l in range(n_layers):\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            for j in range(i):\n",
        "            \t# factor of 2 due to definition of gate\n",
        "                qml.IsingZZ(2*gammas[l]*A[i,j], wires=[i,j])\n",
        "\n",
        "        for i in range(n_nodes):\n",
        "            qml.RX(A[i,i]*betas[l], wires=i)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glOVsqRvjAmi"
      },
      "source": [
        "We can use this ansatz in a circuit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 92,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "0oMs3Tu0jAmi",
        "outputId": "5f59f807-fd37-48a9-a52f-c5ebc6470907"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 58400x2600 with 1 Axes>"
            ],
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          },
          "metadata": {}
        }
      ],
      "source": [
        "n_qubits = 25\n",
        "n_layers = 2\n",
        "\n",
        "dev = qml.device(\"lightning.qubit\", wires=n_qubits)\n",
        "\n",
        "@qml.qnode(dev)\n",
        "def eqc(adjacency_matrix, observable, trainable_betas, trainable_gammas):\n",
        "    \"\"\"Circuit that uses the permutation equivariant embedding\"\"\"\n",
        "\n",
        "    perm_equivariant_embedding(adjacency_matrix, trainable_betas, trainable_gammas)\n",
        "    return qml.expval(observable)\n",
        "\n",
        "\n",
        "A = create_data_point(n_qubits)\n",
        "betas = np.random.rand(n_layers)\n",
        "gammas = np.random.rand(n_layers)\n",
        "observable = qml.PauliX(0) @ qml.PauliX(1) @ qml.PauliX(3)\n",
        "\n",
        "qml.draw_mpl(eqc, decimals=2)(A, observable, betas, gammas)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIHRQVnDjAmi"
      },
      "source": [
        "Validating the equivariance\n",
        "===========================\n",
        "\n",
        "Let\\'s now check if the circuit is really equivariant!\n",
        "\n",
        "This is the expectation value we get using the original adjacency matrix\n",
        "as an input:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "ZCFN2RkSjAmj",
        "outputId": "658c66c7-06d9-40e4-801e-3c8ed85d9cb6"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for A: 0.00021020561796463583\n"
          ]
        }
      ],
      "source": [
        "result_A = eqc(A, observable, betas, gammas)\n",
        "print(\"Model output for A:\", result_A)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ncmkAwH-jAmj"
      },
      "source": [
        "If we permute the adjacency matrix, this is what we get:\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 94,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "KjwEdmGXjAmj",
        "outputId": "c0a39b8e-7ee8-4832-c6d2-4a0efdf4b10e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A:  -0.2781727038892467\n"
          ]
        }
      ],
      "source": [
        "perm = [2, 3, 0, 1, 4]\n",
        "A_perm = permute(A, perm)\n",
        "result_Aperm = eqc(A_perm, observable, betas, gammas)\n",
        "print(\"Model output for permutation of A: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOIqQmysjAmj"
      },
      "source": [
        "Why are the two values different? Well, we constructed an *equivariant*\n",
        "ansatz, not an *invariant* one! Remember, an *invariant* ansatz means\n",
        "that embedding a permutation of the adjacency matrix leads to the same\n",
        "state as an embedding of the original matrix. An *equivariant* ansatz\n",
        "embeds the permuted adjacency matrix into a state where the qubits are\n",
        "permuted as well.\n",
        "\n",
        "As a result, the final state before measurement is only the same if we\n",
        "permute the qubits in the same manner that we permute the input\n",
        "adjacency matrix. We could insert a permutation operator\n",
        "`qml.Permute(perm)` to achieve this, or we simply permute the wires of\n",
        "the observables!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "id": "MgYVIMP6jAmj"
      },
      "outputs": [],
      "source": [
        "observable_perm = qml.PauliX(perm[0]) @ qml.PauliX(perm[1]) @ qml.PauliX(perm[3])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pb21hBrLjAmj"
      },
      "source": [
        "Now everything should work out!\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "tpzF6L3TjAmj",
        "outputId": "0f13b439-3547-47fa-ba6c-2fec7d01b390"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model output for permutation of A, and with permuted observable:  -0.5690295328948293\n"
          ]
        }
      ],
      "source": [
        "result_Aperm = eqc(A_perm, observable_perm, betas, gammas)\n",
        "print(\"Model output for permutation of A, and with permuted observable: \", result_Aperm)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0wblJk9mjAmj"
      },
      "source": [
        "Et voilà!\n",
        "\n",
        "Conclusion\n",
        "==========\n",
        "\n",
        "Equivariant graph embeddings can be combined with other equivariant\n",
        "parts of a quantum machine learning pipeline (like measurements and the\n",
        "cost function). [Skolik et al.\n",
        "(2022)](https://arxiv.org/pdf/2205.06109.pdf), for example, use such a\n",
        "pipeline as part of a reinforcement learning scheme that finds heuristic\n",
        "solutions for the traveling salesman problem. Their simulations compare\n",
        "a fully equivariant model to circuits that break permutation\n",
        "equivariance and show that it performs better, confirming that if we\n",
        "know about structure in our data, we should try to use this knowledge in\n",
        "machine learning.\n",
        "\n",
        "References\n",
        "==========\n",
        "\n",
        "1.  Andrea Skolik, Michele Cattelan, Sheir Yarkoni,Thomas Baeck and\n",
        "    Vedran Dunjko (2022). Equivariant quantum circuits for learning on\n",
        "    weighted graphs.\n",
        "    [arXiv:2205.06109](https://arxiv.org/abs/2205.06109)\n",
        "2.  Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone,\n",
        "    Patrick J. Coles, Frédéric Sauvage, Martín Larocca and Marco Cerezo\n",
        "    (2022). Theory for Equivariant Quantum Neural Networks.\n",
        "    [arXiv:2210.08566](https://arxiv.org/abs/2210.08566)\n",
        "\n",
        "About the author\n",
        "================\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "seconds = time.time()\n",
        "print(\"Time in seconds since end of run:\", seconds)\n",
        "local_time = time.ctime(seconds)\n",
        "print(local_time)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "HFTIJBPqph2f",
        "outputId": "69104f78-a7e1-47ad-f9a4-b0b98f564e07"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time in seconds since end of run: 1701148058.1719167\n",
            "Tue Nov 28 05:07:38 2023\n"
          ]
        }
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
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      },
      "file_extension": ".py",
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      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "provenance": [],
      "machine_shape": "hm"
    },
    "accelerator": "TPU"
  },
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  "nbformat_minor": 0
}